Task Number 7 Task Description Solution Of Linear System Of Equations Using Gauss Elimination Method Task Details 1 Us 1 (140.47 KiB) Viewed 15 times
Task number 7 Task description Solution of Linear System of equations using Gauss Elimination method. Task details 1. Use the generated linear system of equations that you generated previously according to the general requirements. 2. 3. Draw a figure for the generated system of equations. Solve the generated system of equations Gauss Elimination method and the following pivoting scenarios:- a. Without scaling or pivoting b. With simple pivoting c. With partial pivoting d. With scaled partial pivoting (online) e. With scaled partial pivoting (offline) 4. Extremely detailed solution should be included that shows the results in detail after each elimination process. 5. Provide a table that shows the exact solution, the approximate solution, the absolute error, and the true relative percentage error for each independent variable for each pivoting scenario. General requirements for tasks 7 till 11. The System of Linear equations used in these tasks should satisfy the following rules:- 1. All of the coefficients in the generated system of linear equations (a¡j) should have integer non-zero values. Fractional values are not allowed. 2. To find the right-hand side of each equation (b), set any random integer value for all independent variables (x;). Then substitute these values in the generated equations and find right-hand side of each equation (b). Based on this, all (b) values will be integer values. 3. The entire solution process for any solution method in tasks 7 till 11 must be based on 8 significant figures (8 digits) with rounding. 4. The selected system of linear equations for each group for all tasks from 7 till 11 is fixed as given in the table below. Singular System of three Linear equations with no solutions
General requirements for tasks 7 till 11. The System of Linear equations used in these tasks should satisfy the following rules:- 1. All of the coefficients in the generated system of linear equations (a) should have integer non-zero values. Fractional values are not allowed. 2. To find the right-hand side of each equation (b), set any random integer value for all independent variables (x₂). Then substitute these values in the generated equations and find right-hand side of each equation (b). Based on this, all (b) values will be integer values. 3. The entire solution process for any solution method in tasks 7 till 11 must be based on 8 significant figures (8 digits) with rounding. 4. The selected system of linear equations for each group for all tasks from 7 till 11 is fixed as given in the table below. Singular System of three Linear equations with no solutions Task description Task details 1. Use the generated linear system of equations that you generated previously according to the general requirements. 2. Draw a figure for the generated system of equations. 3. Solve the generated system of equations Gauss Elimination method and the following pivoting scenarios:- a. Without scaling or pivoting b. With simple pivoting Solution of Linear System of equations using Gauss e. With partial pivoting d. With scaled partial pivoting (online) Elimination method e. With scaled partial pivoting (offline) 4. Extremely detailed solution should be included that shows the results in detail after each elimination process. 5. Provide a table that shows the exact solution, the approximate solution, the absolute error, and the true relative percentage error for each independent variable for each pivoting scenario. Task number
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